Two Meanings of Division

When students are first introduced to the concept of division, it is a great opportunity to lay the groundwork for fractions word problems in the future. To this end, we usually let students discover two complementary meanings of division, namely:

  • dividing into n groups, and
  • dividing into groups of n.

The ability to see division in these two visual interpretation comes in handy when dealing with word problems in fractions, e.g.:

  • ½ divided by 4, can be interpreted as half a pizza divided into 4 parts, each part is one-eighth of a pizza.


  • 1½ divided by ½, can be interpreted as 1½ pounds of sugar divided into ½-pound bags, total 3 bags.

The attached worksheet is extracted from the coming week’s 2nd grade resources for our members, with exercise to practice differentiating between both meanings of division using integers values in 2nd grade.

Related Resources

For more related resources, please refer to our Multiplication and Division page.

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